This counterexample shows that our proof of locality is by no means purely group-theoretic.
Namely, in order to obtain strict locality, it is necessary to assume stronger property than strict locality
itself of the original net (wedge-split property or modular nuclearity as above).
The above massless counterexample appears to be related to the subtlety in massless bootstrap program:
the convergence of form factors is typically worse in massless models and even the fundamental
commutativity theorem relies on the behavior of form factors, which is also worse (c.f. [1]}).
Hence if one aims at constructing Wightman fields or Haag-Kastler net out of form factors,
the problem of convergence is inevitable.
